Give an example of a quadratic function that has zeroes at $x=2$ and $x=4$, and that takes the value $6$ when $x=3$. Write your answer in expanded form "ax^2 + bx + c", where a,b,c are replaced by appropriate numbers.
We can write
y = a ( x - 2) ( x - 4) and we know that ( 3, 6) is on the graph so
6 = a ( 3 - 2) ( 3 - 4)
6 = -1 a
a = -6
So we have
y = -6 ( x - 2) ( x - 4)
y = -6 ( x^2 - 6x + 8)
y = -6x^2 + 36x - 48
See the graph here : https://www.desmos.com/calculator/puneh6dg7u
